Electrical conductivity model for quasi-one-dimensional structures
https://doi.org/10.17586/2220-8054-2017-8-2-231-235
Abstract
The electron-impurity scattering coefficient of Bloch waves for one dimensional Dirac comb potential is used for calculating the temperature dependence of conductivity within kinetic theory. We restrict ourselves by scattering on impurities that is also modelled by zero-range potential. The conductivity is obtained by standard averaging in momentum space, it is expressed by integral that is evaluated within temperature expansion.
About the Authors
S. A. BotmanRussian Federation
ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016
S. B. Leble
Russian Federation
ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016
References
1. Dingle R.B. The electrical conductivity of thin wires. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1950, 201 (1067), P. 545.
2. Lal R. Effect of electron-phonon interaction on the resistivity of metallic nanowires. Physical Review B, 2003, 68 (11), P. 115417.
3. Zhang Z., Sun X., et al. Electronic transport properties of single-crystal bismuth nanowire arrays. Physical Review B, 2000, 61 (7), P. 4850–4861.
4. Lin Y., Sun X., Dresselhaus M.S. Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires. Physical Review B, 2000, 62 (7), P. 4610.
5. Wen W., Brongersma S.H., Van Hove M., Maex K. Influence of surface and grain-boundary scattering on the resistivity of copper in reduced dimensions. Applied physics letters, 2004, 84 (15), P. 2838–2840.
6. Natelson D., Willett R.L., West K.W., Pfeiffer L.N. Molecular-scale metal wires. Solid State Communications, 2004, 115 (5), P. 269–274.
7. Botman S., Leble S. Bloch wave — ZRP scattering as a key element of solid state physics computation: 1D example. TASK Quarterly, 2016, 20 (2), P. 197–206.
8. Kolmogoroff A. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung ¨ Mathematische Annalen, 1931, 104 (1), P. 415–458.
9. Newton R.G. Bloch-wave scattering by crystal defects. Journal of mathematical physics, 1991, 32 (2), P. 551–560.
10. Boitsev A., Neidhardt H., Popov I. Dirac operator coupled to bosons. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 332–339.
11. Rosch A., Andrei N. Conductivity of a clean one-dimensional wire. Physical review letters, 2000, 85 (5), P. 1092.
12. Popov I., Kurasov P., et al. A distinguished mathematical physicist Boris S. Pavlov. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 782–788.
13. Bid A., Bora A., Raychaudhuri A.K. Temperature dependence of the resistance of metallic nanowires of diameter ≥ 15 nm: Applicability of Bloch-Gr¨uneisen theorem. Physical Review B, 2006, 74 (3), P. 035426.
Review
For citations:
Botman S.A., Leble S.B. Electrical conductivity model for quasi-one-dimensional structures. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(2):231-235. https://doi.org/10.17586/2220-8054-2017-8-2-231-235